Yes, after thinking about this, the Kenwood HU is "powered" correctly. Meaning it is receiving ACC, CONSTANT, and GND to work (three key wires to power on any radio), so you are able to see it playing a CD. This means the speaker wires are left to test.

How are your grounding your speaker wires? Sorry, I am confused. I hope you meant you connected for example: Front Left speakers

White (Adapter) to White (Kenwood Wire) (positive)
White/Black (Adapter) to White/Black (Kenwood Wire) (negative-ground).

If you connected to your White/Black wire to your Car frame, I think that is the problem...